Automata Theory Part B
Exploring Automata Theory
Test your understanding of Automata Theory with this comprehensive quiz designed for students and enthusiasts alike. With 30 challenging questions, you will gain insights into logical proofs, theorems, and important concepts within the realm of formal languages and computations.
This quiz covers a variety of topics including:
- Pumping Lemma
- Proof Techniques
- Logical Equivalences
- Properties of Integers
Let the statement be “If n is not an odd integer then the square of n is not odd.”, then if P(n) is “n is a not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof, we should prove _________
nP ((n) → Q(n))
n~(P ((n)) → Q(n))
nP ((n) → ~(Q(n)))
nP ((n) → Q(n))
While applying Pumping lemma over a language, we consider a string w that belong to L and fragment it into _______ parts.
3
2
5
4
Which of the arguments is invalid in proving that the sum of two odd numbers is not odd?
3 + 3 = 6, hence true for all
All of the mentioned
2n +1 + 2m +1 = 2(n+m+1) hence true for all
None of the mentioned
______ is used as a proof for irregularity of a language
Pumping lemma
Conjecture
Corollary
None of the mentioned
A proof that p → q is true based on the fact that q is true, such proofs are known as ____
Trivial proof
Direct proof
Contrapositive proofs
Proof by cases
A proof that p → q is true based on the fact that q is true, such proofs are known as _____
Trivial proof
Direct proof
Proof by cases
Contrapositive proofs
In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?
Direct proof
Proof by Contradiction
Vacuous proof
Mathematical Induction
In pumping lemma, If we select a string w such that w∈L, and w=xyz. Which of the following portions cannot be an empty string?
X
Z
Y
all of the mentioned
Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove ___
nP ((n) → Q(n))
n~(P ((n)) → Q(n))
nP ((n) → Q(n))
nP ((n) → ~(Q(n)))
A proof that p → q is true based on the fact that q is true, such proofs are known as …...
Direct proof
Trivial proof
Contrapositive proofs
Proof by cases
When to proof P→Q true, we proof P false, that type of proof is known as:
Direct proof
Contrapositive proofs
Mathematical Induction
Vacuous proof
To prove a statement p is true, you may assume that it is false, and then proceed to show that such an assumption leads a contradiction with a known result. This is called:
Direct proof
Trivial proof
Proof by contradiction
Proof by Induction
Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be
nP ((n) → Q(n))
nP ((n) → Q(n))
n~(P ((n)) → Q(n))
∀n(~Q ((n)) → ~(P(n)))
A theorem used to prove other theorem is known as
Lemma
Conjecture
Corollary
None of the mentioned
For m = 1, 2, …, 4m+2 is a multiple of is known as….:
Lemma
Corollary
None of the mentioned
Conjecture
All of the following statements could be proven with a direct proof EXCEPT: Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ is best represented by….:
~P V ~Q
P ∧ ~Q
P V Q
P ∧ Q
A proof that p → q is true based on the fact that q is true, such proofs are known as….:
Direct proof
Trivial proof
Contrapositive proofs
Proof by cases
The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people….:
x (F (x) → P (x))
x (F (x) ∧ P (x))
x (F (x) ∧ P (x))
x (F (x) → P (x))
A theorem used to prove other theorems is known as ….:
Lemma
Conjecture
Corollary
None of the mentioned
(p →q) ∧ (p →r) is logically equivalent to
p→(q ∨ r)
p→(q ∧ r )
p ∧ (q→r)
P ∧ (q→r)
In proving π as irrational, we begin with assumption √7 is rational in which type of proof?
Direct proof
Direct proof
Proof by Contradiction
Trivial proof
Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove
nP ((n) → Q(n))
nP ((n) → Q(n))
n~(P ((n)) → Q(n))
n(P ((n)) → Q(n))
A proof that p → q is true based on the fact that q is true, such proofs are known as
Direct proof
Proof by Contradiction
Trivial proof
Vacuous proof
(p → r) ∨ (q → r) is logically equivalent to
(p ∧ q) ∨ r
(p ∧ q) → r
(p ∨ q) → r
(p → q) → r
In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?
Proof
Direct proof
Proof by Contradiction
Mathematical Induction
A proof that p → q is true based on the fact that q is true, such proofs are known as
Direct proof
Trivial proof
Proof by cases
Contrapositive proofs
A theorem used to prove other theorems is known as
Lemma
Conjecture
Corollary
None of the mentioned
Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove
nP ((n) → Q(n))
n~(P ((n)) → Q(n))
nP ((n) → Q(n))
nP ((n) → ~(Q(n)))
Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be
∀nP ((n) → Q(n))
n~(P ((n)) → Q(n))
nP ((n) → Q(n))
n(~Q ((n)) → ~(P(n)))
A proof that p → q is true based on the fact that q is true, such proofs are known as:
Direct proof
Trivial proof
Contrapositive proofs
Proof by cases
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